Physiological simulation of blood flow in the aorta: comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models.

Interest in patient-specific blood-flow circulation modeling has increased substantially in recent years. The availability of clinical data for geometric and elastic properties together with efficient numerical methods has now made model rendering feasible. This work uses 3-D fluid-structure interaction (FSI) to provide physiological simulation resulting in modeling with a high level of detail. Comparisons are made between results using FSI and rigid wall models. The relevance of wall compliance in determining parameters of clinical importance, such as wall shear stress, is discussed together with the significance of differences found in the pressure and flow waveforms when using the 1-D model. Patient-specific geometry of the aorta and its branches was based on MRI angiography data. The arterial wall was created with a variable thickness. The boundary conditions for the fluid domain were pressure waveform at the ascending aorta and flow for each outlet. The waveforms were obtained using a 1-D model validated by in vivo measurements performed on the same person. In order to mimic the mechanical effect of surrounding tissues in the simulation, a stress-displacement relation was applied to the arterial wall. The temporal variation and spatial patterns of wall shear stress are presented in the aortic arch and thoracic aorta together with differences using rigid wall and FSI models. A comparison of the 3-D simulations to the 1-D model shows good reproduction of the pressure and flow waveforms.

[1]  C. J. Greenshields,et al.  A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes , 2005 .

[2]  Miguel A. Fernández,et al.  A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid , 2007 .

[3]  F. NOBILE,et al.  An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions , 2008, SIAM J. Sci. Comput..

[4]  John A. Frangos,et al.  Temporal Gradients in Shear, but Not Spatial Gradients, Stimulate Endothelial Cell Proliferation , 2001, Circulation.

[5]  K. Perktold,et al.  Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. , 1995, Journal of biomechanics.

[6]  Reto Meuli,et al.  Estimation of local aortic elastic properties with MRI , 2002, Magnetic resonance in medicine.

[7]  Alfio Quarteroni,et al.  Cardiovascular mathematics : modeling and simulation of the circulatory system , 2009 .

[8]  Toshio Kobayashi,et al.  Influence of wall elasticity in patient-specific hemodynamic simulations , 2007 .

[9]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[10]  Charles A. Taylor,et al.  On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model , 2009, Annals of Biomedical Engineering.

[11]  Alessandro Veneziani,et al.  Reduced models of the cardiovascular system , 2009 .

[12]  Jean-Frédéric Gerbeau,et al.  Simulation numérique du système cardiovasculaire , 2005 .

[13]  A. Quarteroni,et al.  Fluid―structure interaction simulation of aortic blood flow , 2011 .

[14]  Alejandro F. Frangi,et al.  Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity , 2005, IEEE Transactions on Medical Imaging.

[15]  Manuel Doblaré,et al.  Mechanical stresses in abdominal aortic aneurysms: influence of diameter, asymmetry, and material anisotropy. , 2008, Journal of biomechanical engineering.

[16]  F. Grosveld,et al.  Atherosclerotic Lesion Size and Vulnerability Are Determined by Patterns of Fluid Shear Stress , 2006, Circulation.

[17]  Wolfgang A. Wall,et al.  Coupling strategies for biomedical fluid–structure interaction problems , 2010 .

[18]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[19]  K. Digges,et al.  Blunt trauma and acute aortic syndrome: a three-layer finite-element model of the aortic wall. , 2008, European journal of cardio-thoracic surgery : official journal of the European Association for Cardio-thoracic Surgery.

[20]  M. Gimbrone,et al.  Vascular endothelium responds to fluid shear stress gradients. , 1992, Arteriosclerosis and thrombosis : a journal of vascular biology.

[21]  Charles A. Taylor,et al.  Patient-specific modeling of cardiovascular mechanics. , 2009, Annual review of biomedical engineering.

[22]  A Karac,et al.  Validation of a fluid-structure interaction numerical model for predicting flow transients in arteries. , 2009, Journal of biomechanics.

[23]  F. Lazeyras,et al.  Validation of a patient-specific one-dimensional model of the systemic arterial tree. , 2011, American journal of physiology. Heart and circulatory physiology.

[24]  A. Quarteroni,et al.  On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels , 2001 .

[25]  Nikos Stergiopulos,et al.  Arterial Wall Response to ex vivo Exposure to Oscillatory Shear Stress , 2005, Journal of Vascular Research.

[26]  D. A. Mcdonald Blood flow in arteries , 1974 .

[27]  J-F Gerbeau,et al.  External tissue support and fluid–structure simulation in blood flows , 2012, Biomechanics and modeling in mechanobiology.

[28]  Paolo Crosetto,et al.  Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics , 2011, SIAM J. Sci. Comput..

[29]  R. Ogden,et al.  Mechanics of biological tissue , 2006 .

[30]  N. Stergiopulos,et al.  Validation of a one-dimensional model of the systemic arterial tree. , 2009, American journal of physiology. Heart and circulatory physiology.

[31]  Nan Xiao,et al.  Simulation of blood flow in deformable vessels using subject‐specific geometry and spatially varying wall properties , 2011, International journal for numerical methods in biomedical engineering.

[32]  Nikos Stergiopulos,et al.  Pulse Wave Propagation in the Arterial Tree , 2011 .

[33]  Alejandro F Frangi,et al.  Reproducibility of haemodynamical simulations in a subject-specific stented aneurysm model--a report on the Virtual Intracranial Stenting Challenge 2007. , 2008, Journal of biomechanics.

[34]  D. Balzani Polyconvex anisotropic energies and modeling of damage applied to arterial walls , 2006 .

[35]  G. Kassab,et al.  Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment. , 2007, American journal of physiology. Heart and circulatory physiology.